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A085104
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Primes of the form 1 + n + n^2 + n^3 +...+ n^k, n > 1, k > 1.
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8
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7, 13, 31, 43, 73, 127, 157, 211, 241, 307, 421, 463, 601, 757, 1093, 1123, 1483, 1723, 2551, 2801, 2971, 3307, 3541, 3907, 4423, 4831, 5113, 5701, 6007, 6163, 6481, 8011, 8191, 9901, 10303, 11131, 12211, 12433, 13807, 14281, 17293, 19183, 19531, 20023
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Primes that are base-b repunits with three or more digits for at least one b >= 2: Primes in A053696. Subsequence of A000668 UNION A076481 UNION A086122 UNION A165210 UNION A102170 UNION A004022 UNION ... (for each possible b). [From Rick L. Shepherd (rshepherd2(AT)hotmail.com), Sep 07 2009]
Brazilian primes - see A125134.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..3880
Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38.
Bernard Schott, Les nombres brésiliens, Reprinted from Quadrature, no. 76, avril-juin 2010, pages 30-38, included here with permission from the editors of Quadrature.
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EXAMPLE
| 13 is a term as 1+3+9.
31 is a term as 1+2+4+8+16.
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MATHEMATICA
| max = 140; maxdata = (1 - max^3)/(1 - max); a = {}; Do[i = 1; While[i = i + 2; cc = (1 - m^i)/(1 - m); cc <= maxdata, If[PrimeQ[cc], a = Append[a, cc]]], {m, 2, max}]; Sort[DeleteDuplicates[a]] (* Lei Zhou, Feb 08 2012 *)
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CROSSREFS
| Cf. A002383, A189891 (complement), A125134.
Cf. A003424 (n restricted to prime powers), A059055
Cf. A053696, A000668, A076481, A086122, A165210, A102170, A004022. [From Rick L. Shepherd (rshepherd2(AT)hotmail.com), Sep 07 2009]
Sequence in context: A087196 A074963 A110912 * A162652 A181141 A031158
Adjacent sequences: A085101 A085102 A085103 * A085105 A085106 A085107
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KEYWORD
| nonn,changed
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AUTHOR
| Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), Jul 03 2003
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EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jan 26 2005
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